1. FIELD OF THE INVENTION
The present invention relates to ion implantation for impurity doping in a semiconductor manufacturing process and, more particularly, to an ion implantation simulation method Of calculating a distribution of impurity particles which are ion-implanted into a substrate and stop at certain positions because of the energy loss after repetitive collision against the substrate.
2. DESCRIPTION OF THE PRIOR ART
Ion implantation simulation using a Monte Carlo method (to be referred to as "Monte Carlo ion implantation simulation" hereinafter) is described in Ryo Dan, "Process Device Simulation Technology", p. 60. In this ion implantation simulation, a process that implanted ions scatter and lose energy while colliding against atomic nuclei and electrons in the substrate is calculated using a probabilistic technique. More specifically, a random number is generated for every collision process to determine the relative position with respect to a target atom, i.e., a collision parameter. Scattering (energy transition and direction) of the implanted ions is calculated on the basis of the collision parameter, thereby obtaining the distribution of impurity particles which have finally stopped in the substrate. In this specification, calculation of the scattering process of implanted ions using the above-described Monte Carlo method will be referred to as "scattering calculation" hereinafter.
To accurately calculate the distribution using this simulation method, a lot of trajectories of implanted ions must be calculated, resulting in a very long calculation time. A solution to this problem is described in S. H. Yang et al., "A More Efficient Approach for Monte Carlo Simulation of Deeply-Channeled Implanted Profiles in Single-Crystal Silicon", NUPAD V, pp. 97-100, (1994).
According to this technique, Monte Carlo ion implantation simulation is performed first using a certain number of sample particles to obtain an impurity profile as shown in FIG. 1A. Next, with reference to the resultant profile, positions in the depth direction where the sample particles are divided are determined. These positions are represented by d.sub.1, d.sub.2, and d.sub.3 in FIG. 1B. Sample particles which have reached the depths d.sub.1, d.sub.2, and d.sub.3 are divided, and the Monte Carlo ion implantation simulation is performed again. With this process, a profile whose tail portion has minimum noise can be obtained, as shown in FIG. 1B.
In the conventional simulation method, however, simulation can hardly be extended to two or three dimensions. The reason for this is as follows. To extend simulation to two or three dimensions, a function of determining a two- or three-dimensional line segment sequence or plane is required to divide sample particles.